Abstract
In a lot of geometric situations we need to work with families of varieties. In this talk we focus on families of singular Kähler-Einstein metric.
In particular we study the case of a family of Kähler varieties and we develop the first steps of pluripotential theory in family,
which will allow us to have a control on the C^0 estimate when the complex structure varies.
This type of result will be applied in different geometric contexts.
This is a joint work with V. Guedj and H. Guenancia.